Question

Planes are drawn parallel to the coordinate planes through the points (3,0-1) and (- 2, 5, 4). Find the lengths of the edges of the parallelopiped so formed.

Answer 1

Points $A(3,0,-1),B(-2,5,4)$

Planes are drawn parallel to $xy,yz$ and $zx$ plane from points $A$ and $B$ to from parallel piped.

$\therefore$ planes are $x=3,y=0,z=-1$ through $A$

$x=-2,y=5,z=-1$ through $B$

Distances between planes will be lengths of figure.

$\therefore$ length along $x=|3-(-2\left)\right|=5$

$\therefore$ length along $y=|5-0|=5$

$\therefore$ length along $z=|-1-4|=5$

$\therefore$ dimensions of parallelopiped will be $(5\times 5\times 5)$